Numberphile Maths
Number Theory
Level
1
What is the units digit of the fifth root of 4984209207?
Use of a calculator is prohibited. Not that I'll know.
The answer is 7.
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Since we only care about the units digit, we only have to worry about the units digit of the fifth root. So we just have to find a number whose fifth power has a 7 in the units digit. 1^5 mod 10 = 1 2^5 mod 10 = 2 3^5 mod 10 = 3 4^5 mod 10 = 4 . . . We realize that all these digits to the fifth power have that digit as the units digit. So the answer is 7